The goal of the “busy beaver” game is to find the longest-running computer program. Its pursuit has surprising connections to some of the most profound questions and concepts in mathematics. The rub is that BB(27) is such an incomprehensibly huge number that even writing it down, much less running the Goldbach-falsifying machine for that many steps, isn’t remotely possible in our physical universe. Nevertheless, that incomprehensibly huge number is still an exact figure whose magnitude represents “a statement about our current knowledge” of number theory.

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